I was unclear about the case and the meaning of Domino.So I checked the grammar, and found that

1. (if dative,) this may be the dative of whither, since the following lines have jubilemus Deo salutari nostro and jubilemus ei, which are taking this usage of dative.

2. (if dative,) this may be the dative of interst, meaning rejoice in us somehow benefits the God.

3. (if ablative,) this may be the ablative of cause. This usage is mainly applied to the verbs of emotion, and the ablative noun seems to be mostly abstractive, like "by the love of you", "from hate", "from hope", etc.(This dative also expresses the cause of event.) But, I could not make sure if this dative is used in personal noun, like Guillelmo, Ciceroni, tibi, Domino ("because of the Lord").So I need to be informed about if this dative is used in personal noun.

Are these all possible meaning ? Or ?Do you have other understanding ?

It's definitely not a classical construction, so don't go looking in a classical grammar (e.g. dat. of interest). I believe this use mirrors the confiteor + dat. construction, which according to L&S means:

About the simularity with confiteor + dat., I'm not convinced very much, because exsulto and confiteor are so much different in meaning...By the way, the dat. which confiteor takes is the direct object of the verb ?Once I checked this word confiteor in L&S and saw this ecclesiastic usage, but I didn't understand well.Someone here told me it meant "to confess the faith in...".

I too, thought this exsulto + dat. construction would be a copy from Greek or Hebrew one.I'll check later the Biblegateway page for this psalm where there are Latin text and Greek text side by side,and report it to you.

There was no Greek Old Testament page in the Biblegateway.So I searched the web.It was confusing that the usual psalm94 was in Septuagint Psalm95.

exsultemus Domino in psalm94 was in Septuagint psalm 95 ἀγαλλιασώμεθα τῷ κυρίῳ.agalliazometha seems to have the same meaning and usage with agallomai.And agallomai means "glory, exalt in a thing" used with dat..exalt in his horse and chariot.exalt in her beautiful face.These nouns are dat..

Then, this Domino is no proper Latin ?Could all the Latin speakers understand exsultemus Domino ?

Then (this is an off-topic question about the history of Latin) people of the time brought various kinds of Latin from everywhere ?And a man in Rome could hear strange forms of Latin brought from some different regions, like Egypt, Romania, England, Greece, and understand them easily ?How ?

I wasn't there to test, but I think the Latin speakers of the time could understand it more or less like today's English speakers can understand the Douay–Rheims version of the Bible.

Then people of the time brought various kinds of Latin from everywhere ?And a man in Rome could hear strange forms of Latin brought from some different regions, like Egypt, Romania, England, Greece, and understand them easily ?

Right. Today in London or New York there are many foreign immigrants and they speak an English which is a little different from that of the natives, yet they manage to communicate. Have you ever met a foreigner in Japan who tries to communicate in Japanese with you? Do you understand him? He might sound funny to you, but I bet you manage.

I expected as much. I bet you'll find the same if you look up confiteor's equivalent.

Vulgate Latin is a very peculiar thing. It is indeed "impure" in the sense that it is heavily tainted by Greek and Hebrew, especially the Gallican psalter, but that is not necessarily a bad thing considering the purpose it served. Christians have always been picky about the wording in translations, and usually prefer more literal renderings to figurative ones. Add to this the fact that early Christians considered the Septuagint to be inspired as much (or more) than the Hebrew, and you have the explanation why they preferred to compromise on the quality of the Latin than abandon the specific wording.

Right. Today in London or New York there are many foreign immigrants and they speak an English which is a little different from that of the natives, yet they manage to communicate. Have you ever met a foreigner in Japan who tries to communicate in Japanese with you? Do you understand him? He might sound funny to you, but I bet you manage.

Yes, I understand him.If his speech is grammatically very inaccurate, I would understand him, a little vaguely.I think I would get a better understanding if he speaks in an almost correct grammar.Wordings which sound odd to the natives would be no problem.

Vulgate Latin is a very peculiar thing. It is indeed "impure" in the sense that it is heavily tainted by Greek and Hebrew, especially the Gallican psalter, but that is not necessarily a bad thing considering the purpose it served. Christians have always been picky about the wording in translations, and usually prefer more literal renderings to figurative ones. Add to this the fact that early Christians considered the Septuagint to be inspired as much (or more) than the Hebrew, and you have the explanation why they preferred to compromise on the quality of the Latin than abandon the specific wording

I see.Is that sort of traditional that academic translations are in many cases mere literal transcriptions and don't seem to try to understand the sentences and convey the understanding of the translators ? Then it is doubtful that people of the time understood exsultemus Domino. They would just accept the strange phrase, like learners of something or believers in a religion just memorize the phrases whose meanings are veiled. Though teachers would give comments on them, the phrases themselves are beyond the personal understanding.